some math problem about simplifing expression?

Question

can anybody tell me the result of this expression?
(y/2+z/3)(y/2+z/3)

the answer from my keybook is y to the second power/4+y to the Z power/3+Z to the second power/9

but I just don't understand why it's y to the Z power, it isn't logical, is it the key wrong?

Answer 1

(y/2+z/3)(y/2+z/3)
Use the FOIL method to multiply this out:
(y/2)(y/2) + (y/2)(z/3) + (z/3)(y/2) + (z/3)(z3)
= y²/4 + yz/6 + yz/6 + z²/9
= y²/4 + 2y/6 + z²/9
= y²/4 + yz/3 + z²9

So it looks like the middle term should be a yz/3 (y multipled by z divided by 3) and NOT y to the z power. Hey, books make mistakes sometimes ;-)

Answer 2

Yes, I think the key is wrong. It should be y to the second power/4+y times z/3+Z to the second power/9. Good luck.

Answer 3

((y/2) + (z/3))((y/2) + (z/3)
(y/2)^2 + (yz/6) + (yz/6) + (z/3)^2
(y/2)^2 + 2(yz/6) + (z/3)^2
(y/2)^2 + (yz/3) + (z/3)^2

This is the same as saying

((y^2)/4) + (yz/3) + ((z^2)/9)

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by the way, yz doesn't mean y to the z power, it means that the 2 variables are being multiplied

Assuming that your key doesn't show y^z, whereas the z is a little z in the top right of y, then the answer in the book is correct.

Answer 4

y to the 2nd power/4 + yz/3 + z to the 2nd power/9

Answer 5

Just FOIL it:
y^2/4+yz/3+z^2/9

Answer 6

(y/2+z/3)(y/2+z/3) =
(1/4)y^2 + (1/3)yz + (1/9)z^2

Your keybook has a misprint. It should be y*z, not y^z

Answer 7

(y/2+z/3)(y/2+z/3)
Using distributive law:

(y/2*y/2)+(z/3*y/2)+(z/3*y/2)+(z/3*z/3)
= y^2/4 + zy/3 + z^2/9